1. **State the problem:** We have the function $f(x) = 6x - 50$ which represents the profit in dollars when selling $x$ shirts. We need to find $f(-2)$, $f(7)$, and $f(12.5)$ and interpret these values in context. 2. **Calculate $f(-2)$:** $$f(-2) = 6(-2) - 50 = -12 - 50 = -62$$ Interpretation: If the company sells -2 shirts (which is not possible), the profit would be -62 dollars. This does not make sense in the real-world context because you cannot sell a negative number of shirts. 3. **Calculate $f(7)$:** $$f(7) = 6(7) - 50 = 42 - 50 = -8$$ Interpretation: If the company sells 7 shirts, they would make a profit of -8 dollars, meaning a loss of 8 dollars. This makes sense as selling few shirts might not cover costs. 4. **Calculate $f(12.5)$:** $$f(12.5) = 6(12.5) - 50 = 75 - 50 = 25$$ Interpretation: If the company sells 12.5 shirts (assuming fractional shirts can be interpreted as average or partial sales), they would make a profit of 25 dollars. This is reasonable in context. 5. **Determine appropriate domain:** Since selling a negative number of shirts is impossible, the domain must be $x \geq 0$. Also, since selling fractional shirts may not be practical, the domain could be restricted to non-negative integers $x \in \{0,1,2,\ldots\}$ if only whole shirts are sold. **Final answers:** - $f(-2) = -62$, not meaningful in context. - $f(7) = -8$, loss of 8 dollars. - $f(12.5) = 25$, profit of 25 dollars. - Appropriate domain: $x \geq 0$ (non-negative real numbers) or $x \in \mathbb{Z}_{\geq 0}$ (non-negative integers) depending on context.